Here's some suggestions with the location of each in mind...
Circle Line boat trip (3 hours around Manhattan on the Hudson and East River) http://www.newyorkcity.uk/boat-tours-in-new-york/
Pier 83 12th Avenue between 42nd and 43rd Street - must book!
Lunch at the Empire Diner http://empire-diner.com/ (no need to book)
210 10th Avenue corner 22nd Street and 10th Avenue
Empire State Building – must book! http://www.esbnyc.com/
5th Avenue between 33rd and 34th Street
Times Square – “Times Square is a major commercial intersection and a neighborhood in Midtown Manhattan, New York City. It is located at the junction of Broadway and Seventh Avenue, and stretches from West 42nd to West 47th Streets.”
Statue of Liberty/Ellis Island Boat tour from Battery Park http://www.libertyellisfoundation.org/
Lunch at Ellen’s Stardust Diner – famous novelty restaurant http://www.ellensstardustdiner.com/ 1650 Broadway and 51st Street - must book!
Fifth Avenue! Drop off at Rockefeller Center. Radio City Music Hall same area. Walk up Fifth Avenue to the where the famous toy store FAO Schwartz used to be. It has unfortunately closed down. It has now been taken over by none other than Apple! 5th Avenue at 58th Street. Walk across the road to Central Park – have a wander - there's lots to see!
Soho – shopping morning! West Broadway, Spring Street, Mercer Street, Prince Street – loads of high street and boutique shops
Lunch – Balthazar – 80 Spring Street
Taxi to Bloomingdales (take passport to Customer Services for 10% discount on the day)
Serendipity - http://www.serendipity3.com/ 225 East 60th Street between 2nd and 3rd Avenue - Great ice cream!
Guggenheim Museum – 5th Avenue and 89th Street (closed Thursdays)
Sprinkles Cup Cakes – use ATM outside shop for a fab experience – gorgeous cakes! http://www.sprinkles.com/cupcake-atm Lexington Avenue between 60th and 61st Street
American Museum of Natural History – Central Park West at 79th Street
Metropolitan Museum of Art - Fifth Avenue between 80th and 84th Streets
Highline and Meatpacking District
“The High Line is a 1.45-mile-long New York City linear park built in Manhattan on an elevated section of a disused New York Central Railroad spur called the West Side Line. Inspired by the 3-mile Promenade plantée, a similar project in Paris completed in 1993, the High Line has been redesigned and planted as an aerial greenway and rails-to-trails park. It runs from Gansevoort Street – three blocks below 14th Street – in the Meatpacking District, through Chelsea”
There are numerous boutique and designer stores in this area.
Lunch or Dinner – Pastis http://www.pastisny.com/ 9, 9th Avenue. Booking recommended – very famous
Little Italy and Chinatown to have a mooch.
http://www.viator.com/New-York-City-tourism/New-York-City-Bus-Tours-tours-tickets/d687-t8635?pref=204&aid=m3253 Best to pre book
Check out the link below for discounts on trips and attractions around New York
These days can be swapped around to suit .. depending on which day you start out on!